In Empire Strikes Back Cloud City is shown to be a mining colony for tibanna gas, and that's it.
However, in most books that refer to Cloud City, they mention that it is a resort and casino city. When did this first start?
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New canon references appear to be introduced in these properties:
Star Wars, Absolutely Everything You Need to Know (reference)
Empire's End (novel)
In terms of Legends era - as far as "official" - StarWars.com referenced gambling on Cloud City in 1999:
Additionally, further back, there seem to be several references in West End RPG materials: